Overview
The averaging method will run a path based attribution over every possible ordering of factors, and the average the results.
Example
{% f(x_1,x_2) = x_1 x_2 %}
Then we have
{% f(0,0) = 0 %}
{% f(2,2) = 4 %}
The averaging method will run the path based attribution for both orderings (x then y, y then x)
and then average the results
Path 1
{% \Delta f_x = f(2, 0) - f(0,0) = 0 %}
{% \Delta f_y = f(2, 2) - f(2,0) = 4 %}
Path 2
{% \Delta f_y = f(0, 2) - f(0,0) = 0 %}
{% \Delta f_y = f(2, 2) - f(0,2) = 4 %}
Results
After averaging the results in the example above, we get the following attribution.
- {% \Delta_x = 2 %}
- {% \Delta_y = 2 %}
Note that the attribution attributes the full change in the function, and produces a unique balanced result.